A comparative study of crumpling and folding of thin sheets

Abstract

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly ine cient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the sti ness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We nd that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.

5 pages

References in corpus (6)

• The structure of suspended graphene sheets
• Geometric Mechanics of Curved Crease Origami
• Morphological Phases of Crumpled Wire
• Crumpling under an ambient pressure
• Energy distributions and effective temperatures in the packing of elastic sheets
• Crumpled Wires and Liouville Field Theory

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• Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems
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• A sheet on deformable sphere: "wrinklogami" patterns suppress curvature-induced delamination
• Wrinkles, folds and plasticity in granular rafts
• Plasticity and Aging of Folded Elastic Sheets
• Compaction of Quasi One-Dimensional Elastoplastic Materials
• A model for the fragmentation kinetics of crumpled thin sheets
• Self-Ordering of Buckling, Bending, Bumping Beams
• Furrows in the wake of propagating d-cones
• Circle packing in regular polygons
• A relaxation constant in the folding of thin viscoelastic sheets
• Simulation of crumpled sheets via alternating quasistatic and dynamic representations
• Universal scaling law of an origami paper spring
• Packing of elastic rings with friction
• Unpacking of a crumpled wire from two-dimensional cavities
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Crumpling an elasto-plastic thin sphere
• Deformation of loops in 2D packing of flexible rods
• Memory in cyclically crumpled sheets
• Packing loops into annular cavities
• Vulnerability of Transport through Evolving Spatial Networks